Do consequentialists generally hold as axiomatic that there must be a morally preferable choice (or conceivably multiple equally preferable choices) in a given situation? If so, could somebody point me to a deeper discussion of this axiom (it probably has a name, which I don't know.)
Not explicitly as an axiom AFAIK, but if you're valuing states-of-the-world, any choice you make will lead to some state, which means that unless your valuation is circular, the answer is yes.
Basically, as long as your valuation is VNM-rational, definitely yes. Utilitarians are a special case of this, and I think most consequentialists would adhere to that also.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.